14: J. & Stevens — New Form of Physical Pendulum. 



Art. II. — A New Form of Physical Pendulum; by 



James S. Stevens. 



In the determination of g by the common form of physical 

 pendulum an error is introduced on account of the fact that 



the knife-edges and clamp affect the 

 moment of inertia and the center of 

 gravity of the pendulum, and in con- 

 sequence the period. A form of pen- 

 dulum in which these errors are 

 eliminated has been found satisfac- 

 tory in my laboratory work. A hole 

 was bored through a brass cylindri- 

 cal rod, about 8 cms. from one end. 

 The knife-edges for the support of 

 the pendulum were screwed a little 

 way into the hole, and their mass 

 adjusted so that they offset the mass 

 of the brass bored out. This is rep- 

 resented at a in the sketch. In this 

 manner the center of gravity of the 

 system remains at the position of the 

 center of gravity of the original bar. 

 The source of error would be en- 

 tirely removed if the center of oscil- 

 lation of the triangular knife-edges 

 were in the same horizontal plane as 

 that of the removed cylinder. If 

 we call the radius of the cylinder r, the distance of the center 

 of oscillation to the point of suspension is in the case of the 

 triangle f r, and in the case of the cylinder f r. Allowing for 

 the relative densities of the steel and brass, the knife-edges 

 may be so constructed and inserted that this result may be 

 brought about. If, however, this error is neglected, the 

 effect will be a raising of the center of oscillation in the 

 region from which the brass has been removed, of J r. 



In the pendulum used r is about one-half a centimeter. 

 The bar is one meter long and therefore the true length of the 

 pendulum may be taken as approximately sixty-two centime- 

 ters. Therefore the error in g due to the error under consid- 

 eration would not exceed 0*03 cm. This is of an order more 

 precise than is usually obtained by any method of finding g in 

 the laboratory. 



